I'm actually surprised we didn't carve up Mexico more. During the 19th Century our policy was to send in the white people, in droves (it's ok when Anglo-Saxons migrate. No one else though. This is still the 19th Century) and have them destabilize the local government and/or have a revolution. Set up an independent republic. Have republic take a vote on whether to become a part of the United States.

Since a majority of the citizens are now Anglo-Saxons from the United States, the vote's going to end up being yes. Texas and Hawaii are notable for this.